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An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the...
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Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This...
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Outliers are observed data points that are far from the least squares line. They have unusual values and need to be examined carefully. Though an outlier may result from erroneous data, at other times, it may hold valuable information about the population under study and should be included in the data. Hence, it is crucial to examine what causes a data point to be an outlier.
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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
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A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
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Shape outlier detection and visualization for functional data: the outliergram.

Ana Arribas-Gil1, Juan Romo2

  • 1Departamento de Estadística, Universidad Carlos III de Madrid, Getafe 28903, Spain ana.arribas@uc3m.es.

Biostatistics (Oxford, England)
|March 14, 2014
PubMed
Summary
This summary is machine-generated.

We introduce a novel method for identifying unusual curve shapes in functional data analysis. This approach helps detect subtle shape outliers, which are often hidden within datasets, improving data visualization and analysis.

Keywords:
Depth for functional dataOutlier visualizationRobust estimationTime course microarray data

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Identifying shape outliers in functional data is challenging, as they are often masked by magnitude outliers.
  • Existing methods struggle to effectively distinguish curves with aberrant shapes from the majority data.

Purpose of the Study:

  • To propose a new method for visualizing and detecting shape outliers in functional data.
  • To develop an algorithm for robust shape outlier detection.
  • To assess the utility of the proposed visualization tool and algorithm.

Main Methods:

  • Exploiting the relationship between two functional data depth measures.
  • Developing a visualization tool called the 'outliergram'.
  • Creating an algorithm for shape outlier detection based on data depth.

Main Results:

  • The outliergram effectively visualizes curves by shape.
  • The proposed algorithm demonstrates reliable performance in shape outlier detection through simulation studies.
  • The method was successfully applied to evaluate cluster quality in time course microarray data.

Conclusions:

  • The new method provides an effective way to visualize and detect shape outliers in functional data.
  • The outliergram and detection algorithm offer valuable tools for functional data analysis and quality assessment.
  • This approach enhances the understanding of complex datasets, particularly in fields like bioinformatics.